As well know in category theory (see Mac Lane book) there are (very useful, and theoretically deep) coherent theorem for various categorical setting: monoidal, symmetric monoidal, braided monoidal (tortile..) bicategory, and pseudofunctor (coherence of canonical morphisms of a pseudofunctors and these of its codomain bicategory, a further case about is ifrations by clivage...).

What about the (partial of course) coherence criterion of a lax.functor between bicategories (lax. generalization of the pseudo.functor result )?